You don't want to replace User SID's in Dynamics Database Since Object SID's won't change by renaming the existing domain. The important part here to reconfigure your SQL Server, you need to enable SA (Builtin SQL Server Account) and remove all the domain accounts before renaming the domain. also once
you rename the domain SQL Server will Stops. after renaming you have to change the SQL Server Service account and start SQL Server Service. then you can log in and Add Accounts (under a new domain )to the SQL Server as the first step. Once your SQL server Up and Running you can change Network Domain in " "USERINFO "Table.
Once you complete SQL Server configuration then go to AX Server Configuration Utility Select SQL Server Again. Make sure you changed AX AOS service Account (under new domain) first before starting. Once your AOS Started, Change .NET connector Settings.
then you need to do changes if you are facing any issue with SSAS, SSRS, Enterprise Portal.
The best way to do this by creating Test Environment, If you are using Physical Servers Just convert your Servers in to Virtual using P2V conversion using Disk2VHD tool (docs.microsoft.com/.../disk2vhd) and then create a Test Environment in Different Network Subnet or Isolated Network to avoid IP /NETBIOS Name Conflict.
Hope this information will help.
Thanks ,
Amith Prasanna